2RaµijyjdxA A dxµ ®ei E 02(X) ®Y. 4. LINEAR CONNECTIONS 43 for any section s of the vector bundle Y -* X and any two vector fields T and T' on X. 4) in order to introduce the curvature of connections on modules and sheaves (see Chapter 8). Some standard operations with linear connections should be recalled. 1) on Y. Then there is a unique linear connection P* on the dual vector bundle Y* -* X such that the diagram JlY X J1Y* _ *T*X x R X 1 rxr* YxY* X x x 0 commutes.